Wilcoxon signed-rank test

About: Wilcoxon signed-rank test is a research topic. Over the lifetime, 1953 publications have been published within this topic receiving 99221 citations. The topic is also known as: Wilcoxon T test & Wilcoxon test.

The meaning and use of the area under a receiver operating characteristic (ROC) curve.

Abstract: A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect difference...

Statistical Comparisons of Classifiers over Multiple Data Sets

Abstract: While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all but ignored. This article reviews the current practice and then theoretically and empirically examines several suitable tests. Based on that, we recommend a set of simple, yet safe and robust non-parametric tests for statistical comparisons of classifiers: the Wilcoxon signed ranks test for comparison of two classifiers and the Friedman test with the corresponding post-hoc tests for comparison of more classifiers over multiple data sets. Results of the latter can also be neatly presented with the newly introduced CD (critical difference) diagrams.

A method of comparing the areas under receiver operating characteristic curves derived from the same cases.

Abstract: Receiver operating characteristic (ROC) curves are used to describe and compare the performance of diagnostic technology and diagnostic algorithms. This paper refines the statistical comparison of the areas under two ROC curves derived from the same set of patients by taking into account the correlation between the areas that is induced by the paired nature of the data. The correspondence between the area under an ROC curve and the Wilcoxon statistic is used and underlying Gaussian distributions (binormal) are assumed to provide a table that converts the observed correlations in paired ratings of images into a correlation between the two ROC areas. This between-area correlation can be used to reduce the standard error (uncertainty) about the observed difference in areas. This correction for pairing, analogous to that used in the paired t-test, can produce a considerable increase in the statistical sensitivity (power) of the comparison. For studies involving multiple readers, this method provides a measure...

A generalized Wilcoxon test for comparing arbitrarily singly-censored samples

Abstract: H2: F1(t) F2(t) (t F2(t) (t < T). The asymptotic efficiency of the test relative to the efficient parametric test when the distributions are exponential is at least 0 75 and increases with degree of censoring. When Ho is true, the test is not seriously affected by real differences in the percentage censored in the two groups. Some comparisons are made for five cases of varying degrees of censoring and tying between probabilities from the exact test and those from the proposed test and these suggest the test is appropriate under certain conditions when the sample size is five in each group. A worked example is presented and some discussion is given to further problems.